Search results for "Second derivative"
showing 10 items of 37 documents
Perturbative treatment of scalar-relativistic effects in coupled-cluster calculations of equilibrium geometries and harmonic vibrational frequencies …
2007
An analytic scheme for the computation of scalar-relativistic corrections to nuclear forces is presented. Relativistic corrections are included via a perturbative treatment involving the mass-velocity and the one-electron and two-electron Darwin terms. Such a scheme requires mixed second derivatives of the nonrelativistic energy with respect to the relativistic perturbation and the nuclear coordinates and can be implemented using available second-derivative techniques. Our implementation for Hartree-Fock self-consistent field, second-order Moller-Plesset perturbation theory, as well as the coupled-cluster level is used to investigate the relativistic effects on the geometrical parameters an…
Relativistic corrections to electrical first-order properties using direct perturbation theory.
2008
Direct perturbation theory (DPT) is applied to compute relativistic corrections to electrical properties such as dipole moment, quadrupole moment, and electric-field gradient. The corrections are obtained as second derivatives of the energy and are given via method-independent expressions that involve the first derivative of the density matrix with respect to the relativistic perturbation as well as property integrals with additional momentum operators. Computational results obtained using Hartree-Fock (HF), second-order Moller-Plesset (MP2) perturbation theory, and the coupled-cluster singles and doubles approach augmented by a perturbative treatment of triple excitations are presented for…
Direct perturbation theory in terms of energy derivatives: Fourth-order relativistic corrections at the Hartree–Fock level
2011
In this work, the quantum-chemical treatment of relativistic effects by means of direct perturbation theory is extended from its lowest order, DPT2, to the next higher order, DPT4. The required theory is given in terms of energy derivatives with the DPT4 energy correction defined as the corresponding second derivative with respect to the relativistic perturbation parameter λ(rel) = c(2) and c as the speed of light. To facilitate the implementation in standard quantum-chemical program packages, a general formulation of DPT starting from a nonrelativistic Lagrangian is developed, thereby expanding both wave function and operators in terms of λ(rel). The corresponding expressions, which incorp…
Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity
2011
We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\dagger]=0$ and $x^\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as $h_1$ and whose eigenvectors are related to those of $h_1$ by $x^\dagger$. Here we extend this procedure to build up a second hamiltonian, whose eigenvalues are different from those of $h_1$, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian hamiltonians.
Investigation of Inspiratory Pressure-Volume Curves on Mechanically Ventilated Patients Using Least Square Polynomial Fit
1988
Abstract An on-line method for the registration of pressure volume 1 oops TrT mechanically ventilated patients was developed using a personal computer with analog/digital interface. A third order polynomial function was fitted to the measured inspiratory pressure volume pairs. The significance of the fitting procedure was calculated using regression ANOVA. The inflection point of the pressure-volume curve was determinated by calculating the root of the second derivative of the polynomial. The method was teseted on 20 patients without major pulmonary dysfunction and on 6 patients with severe ARDS.
PRINZIPIELLE BEMERKUNGEN ZU THEORIE UND PRAXIS DER METHODE DER ZWEITEN ABLEITUNG BEI DER INTERPRETATION GRAVIMETRISCHER MESSERGEBNISSE
1957
The first part of the paper deals with theoretical considerations concerning the arithmetic mean of gravity values and its use with regard to the derivation of approximation formulae for the second derivative. In order to calculate the second derivative in practice the arithmetic mean. ḡ(r) of a continuum of gravity values on a circle of radius r is approximated by a Taylor polynomial and then replaced by the arithmetic mean gn(r) of n discrete gravity values. Because of the invariance of ġ(r) with regard to rotations of the coordinate system in the horizontal datum plane there exists a lower limit for the number n; this lower limit depends on the degree of the Taylor polynomial used in the…
The Nature of Rest Silanol Groups on the Surfaces of Silica Based Solid Phase Extraction Materials
2013
Author's version of an article in the journal: Advanced Materials Research. Also available from the publisher at: http://dx.doi.org/10.4028/www.scientific.net/AMR.650.66 Chemically bonded solid phase materials are very important in separation chemistry. The chemically modified silica gel contains rest silanol groups that can affect the retention properties when they are used for separation of compounds. Some commercially available solid phase extraction (SPE) materials based on silica gel were analysed for rest silanol groups by near infrared spectroscopy. The combination frequency of the water molecules in the 5500- 5000 cm -1 region was used in identifying the nature of water molecules on…
Rapid determination of baicalin and total baicalein content in Scutellariae radix by ATR-IR and NIR spectroscopy
2013
In this study methods for the quantification of baicalin and total baicalein in Scutellariae radix with near infrared (NIR) spectroscopy and attenuated-total-reflectance mid-infrared (ATR-IR) spectroscopy in hyphenation with multivariate analysis were developed and compared. The reference analysis was performed by high performance liquid chromatography coupled to diode array detection (HPLC-DAD). Different pretreatments like standard normal variate (SNV), multiplicative scatter correction (MSC), first and second derivative Savitzky-Golay were applied on the spectra to optimize the calibrations. A principal component analysis was performed with both spectroscopic methods to distinguish wild …
Random walk approximation of BSDEs with H{\"o}lder continuous terminal condition
2018
In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the L2-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution u of the associated PDE. Here we improve existing results by showing some properties of the second derivative of u in space. peerReviewed
New insights into the surface functionalities and adsorption evolution of water molecules on silica gel surface: A study by second derivative near in…
2010
Accepted version of an article in the journal: Vibrational Spectroscopy. Published version available on Science Direct: http://dx.doi.org/10.1016/j.vibspec.2010.06.003 Surface functionalities and adsorption evolution of water molecules on silica gel samples were studied by second derivative near infrared spectroscopy. Four different silica gel samples with varying surface area were used in this experiment. Each of the dry samples was allowed to equilibrate with surrounding air and the near infrared spectra were accumulated at different time intervals using reflectance technique. The evolved spectra were analysed using second derivative technique to study the adsorption evolution of water mo…